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C3×#26014610 #46798620

order33777
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C33

Aliases

direct productC3×#26014610

Splittings

FittingC3×H(3,𝔽3)×C139 ⋊ C3
SylowC139 ⋊ C3×AΣL(1,𝔽27)

Subgroups

subgroupG/H
centerC32C32⋊(C139⋊C3)
commutator, cosocleC32×C139C33
FrattiniC32C32×C139⋊C3
FittingC3×H(3,𝔽3)×C139C3
socleC32×C139H(3,𝔽3)
hypercenterC3×H(3,𝔽3)C139⋊C3
hypocenterC139C3×AΣL(1,𝔽27)
LCSG ▷ C32×C139 ▷ C3×C139 ▷ C139
UCSC1 ◁ C32 ◁ C33 ◁ C3×H(3,𝔽3)

252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3753

Conjugacy classes & character table

1569 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33777, 244);